To insert a prosthetic socket into the natural acetabulum, the latter has to be ground out. To do so, it has hitherto been necessary to have an open access in the direction of the acetabulum axis in order to be able to apply a grinding instrument with a shank extending in the grinder axis. This applies even in minimally invasive operating techniques (WO 01/91648, U.S. Pat. No. 2,785,673) when a corresponding bore is created through the proximal part of the femur. This is complicated and weakens the femur. For cases where accessibility is poor, grinding instruments are known (U.S. Pat. Nos. 5,176,711; 4,808,185; 6,364,910, not published) in which the drive shaft is located at an angle with respect to the rotation axis of the instrument head. This makes it difficult to exactly align the grinding instrument with the acetabulum axis and to exert the axial machining force. This applies in particular to minimally invasive access when the operating field is difficult to see or cannot be seen.